Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential

ZHANG Zhao; ZHAO Wei-Qin

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2003, Vol. 27> Issue(3) : 215-222

Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential

ZHANG Zhao ^, ,
ZHAO Wei-Qin

Institute of High Energy Physics, CAS, Beijing 100039,China2 China Center of Advanced Science and Technology, Beijing 100080, China

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Abstract：
The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP.

References

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ZHANG Zhao and ZHAO Wei-Qin. Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential[J]. Chinese Physics C, 2003, 27(3): 215-222.

ZHANG Zhao and ZHAO Wei-Qin. Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential[J]. Chinese Physics C, 2003, 27(3): 215-222. shu

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Received: 2002-05-14
Revised: 1900-01-01

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Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential

ZHANG Zhao ^,
ZHAO Wei-Qin

Corresponding author: ZHANG Zhao,

Institute of High Energy Physics, CAS, Beijing 100039,China2 China Center of Advanced Science and Technology, Beijing 100080, China

Received Date: 2002-05-14
Accepted Date: 1900-01-01
Available Online: 2003-03-05

Abstract: The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP.